From AMule Project FAQ
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A network is a group of computers which inter-communicate with each other. In other words, a number of computers which share data between each other form a network.
As such, the ed2k network is a network, because it is the union of several computers which share files. More on this, the internet itself is a network, because it is a group of computers which share data too.
Other examples can be local area networks (also known as LANs) or "virtual" networks such as instant messaging networks or workgroup networks.